A177530 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up.

1, 1, 2, 6, 24, 120, 706, 4844, 37968, 334656, 3278896, 35330098, 415289184, 5288377848, 72522052240, 1065579141202, 16700472769061, 278099720959114, 4903387952699182, 91258390273541562, 1787828412527348984, 36776310494510881628, 792526608079806841508

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Columns k=23,29 of A242784.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 6][t]), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9795419074893388679910049642242424087370823270695747551625158..., c = 1.111068410182136129001099552719852410280865324840041630689... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013